Zeitschrift für Analysis und ihre Anwendungen

In this paper, a nonlinear parabolic equation of the form $u_t=(a(u_x))_x$ for $x\in(0,1),\ t>0,\ a(u_x)=|u_x|^{p-2}u_x$ if $u_x\geq\eta>0,\ 10$, then the solutions blow up in finite time. Moreover, estimates on the blow-up profile (in $x$) and the blow-up rate (in $t$) for $x=1$ are derived.